Research Methodology in Social Sciences

Sixth Meeting

• Comparing groups

• Two samples are dependent if natural matching occurs between two groups. For instance, repeated measurements of same subjects
• Samples are independent if they are drawn independently.

• For large samples, or small samples from random distributions the sampling distribution of \( (\bar{y}_{2}-\bar{y}_{1}) \) has a normal shape, we use t-distribution to estimate standard errors and confidence intervals
• Confidence interval for \( \mu_{2}-\mu_{1} \) will be:
  • \( (\bar{y}_{2}-\bar{y}_{1})+/- t(se) \), where \( se=\sqrt{\frac{{s_{1}^2}}{{n}_{1}}+\frac{{s_{2}^2}}{{n}_{2}}} \)
• Usually, interpreting differences between two groups is usually safer and more interpretable than testing null hypothesis

• \( t=\frac{(\bar{y}_{2}-\bar{y}_{1})-0}{se} \)
• Here we compute test statistic and then look for corresponding p-value

• Fisher's exact test OR Chi-square test

• We use non-parametric tests, such as Wilcoxon-Mann-Whitney test
  • Instead of comparing means, we compare median values